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Question
The population of Bigville increased from 387,480 to 571,533 in the last 7 years. During the same time period, Smallville increased its population by 53.67%. Compare the towns to determine which is growing at the greatest rate and by what factor? (round to nearest hundredth)
Responses
A Bigville by a factor of 1.13Bigville by a factor of 1.13
B Bigville by a factor of 6.17Bigville by a factor of 6.17
C Smallville by a factor of 1.13Smallville by a factor of 1.13
D Smallville by a factor of 6.17Smallville by a factor of 6.17
To determine which town is growing at the greatest rate and by what factor, we need to compare the population growth rate of Bigville and Smallville.
The population of Bigville increased from 387,480 to 571,533 in 7 years.
The population of Smallville increased by 53.67% during the same time period.
To find the factor by which Bigville's population increased, we divide the final population by the initial population:
Factor for Bigville = 571,533 / 387,480 = 1.47 (rounded to nearest hundredth)
To find the factor by which Smallville's population increased, we add 53.67% to 100% to get the decimal form of the growth rate:
Decimal growth rate for Smallville = (53.67 + 100) / 100 = 1.5367
Factor for Smallville = 1.5367 (rounded to nearest hundredth)
Comparing the two factors, we can see that Bigville's population increased by a factor of 1.47, while Smallville's population increased by a factor of 1.54.
Therefore, Smallville is growing at the greatest rate by a factor of 1.54.
The correct answer is:
C Smallville by a factor of 1.13.
The graph shows the number of copies a copier can make. What is the unit rate?
Responses
A 125
1 25
B 4545
C 1515
D 25
To determine the unit rate from the given graph, we need to find the slope of the line representing the number of copies a copier can make.
Looking at the graph, it appears that the line starts at the origin (0,0) and passes through the point (4,100).
The unit rate can be calculated by finding the change in the y-coordinate (number of copies) divided by the change in the x-coordinate (time in minutes).
Change in the y-coordinate = 100 - 0 = 100
Change in the x-coordinate = 4 - 0 = 4
Unit rate = Change in y-coordinate / Change in x-coordinate = 100 / 4 = 25
Therefore, the unit rate is 25.
The correct answer is:
D 25.
3 of 103 of 10 Items
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Question
A line represents a proportional relationship. Which set of points could be on the line?
Responses
A (−4, −2), (2, 1), (6, 3), (14,7)(−4, −2), (2, 1), (6, 3), (14,7)
B (6, 8), (4, 0), (18, 24), (20, 26)(6, 8), (4, 0), (18, 24), (20, 26)
C (3, 6), (4, 8), (9, 4), (11, 2)(3, 6), (4, 8), (9, 4), (11, 2)
D (1, 1), (2, 1), (3, 3), (4, 2)
To determine which set of points could be on the line representing a proportional relationship, we need to check if the ratio of the y-coordinate to the x-coordinate is consistent for each point.
Let's check each set of points:
Set A: (−4, −2), (2, 1), (6, 3), (14, 7)
For each point, let's calculate the ratio of y-coordinate to the x-coordinate:
Ratio for (-4, -2) = (-2) / (-4) = 0.5
Ratio for (2, 1) = 1 / 2 = 0.5
Ratio for (6, 3) = 3 / 6 = 0.5
Ratio for (14, 7) = 7 / 14 = 0.5
All the ratios are 0.5, which means the set of points is proportional.
Set B: (6, 8), (4, 0), (18, 24), (20, 26)
Ratio for (6, 8) = 8 / 6 = 4/3
Ratio for (4, 0) = 0 / 4 = 0
Ratio for (18, 24) = 24 / 18 = 4/3
Ratio for (20, 26) = 26 / 20 = 13/10
The ratios are not consistent. Thus, Set B is not proportional.
Set C: (3, 6), (4, 8), (9, 4), (11, 2)
Ratio for (3, 6) = 6 / 3 = 2
Ratio for (4, 8) = 8 / 4 = 2
Ratio for (9, 4) = 4 / 9 (not simplified)
Ratio for (11, 2) = 2 / 11 (not simplified)
The ratios are not consistent. Thus, Set C is not proportional.
Set D: (1, 1), (2, 1), (3, 3), (4, 2)
Ratio for (1, 1) = 1 / 1 = 1
Ratio for (2, 1) = 1 / 2 = 1/2
Ratio for (3, 3) = 3 / 3 = 1
Ratio for (4, 2) = 2 / 4 = 1/2
The ratios are consistent at 1/2. Thus, Set D is proportional.
Therefore, the set of points that could be on the line representing a proportional relationship is:
D (1, 1), (2, 1), (3, 3), (4, 2).
What is the unit rate expressed in the graph?
Responses
A 2 miles/minute2 miles/minute
B 5 miles/minute5 miles/minute
C 52
miles/minute5 2 miles/minute
D 25
miles/minute